Is it possible that a run can be verified if only the time is shown (video format)?

I am asking this because sometimes we may not record the run but get a pb/wr.

No, if you don't want to record full sessions, you can use a replay buffer system, such as the one built into OBS, or other alternatives such as Nvidia Shadowplay or medal.tv

How does the replay buffer system work? Is medal.tv also the same?

Does it record the previous few seconds?

It keeps a buffer of the amount of time you've set it to, then you press a hotkey, and it saves that buffer as a replay/clip. I haven't personally used medal.tv, but I believe it is a same kind of system.

Here's a few tutorials for OBS and Shadowplay respectively:

Thanks :)